Precalculus word problem

Question

Construct a polynomial function with the following properties: fifth degree, 3 is a zero of multiplicity 3, -4 is the only other zero, leading coefficient is 4 

Answer 1

P(x) = 4(x-3)³(x+4)²

3 is a zero with multiplicity 3

-4 is the only other zero, and it has multiplicity 2

Answer 2

f(x) = 4(x-3)^3 (x+4)(x-k) for any real number k.

The polynomial is 4x^5 - 4(5+k)x^4 _ 4(5k-9)x^3 + 4(9k+81)x^2+36(9k-12)x+432k

Answer 3

One of these things is not like the other. Given that the degree is 5 and there are as many zeroes as there are degrees, this doesn't add up. 3 with a multiplicity of 3. That is (x-3)(x-3)(x-3). The other zero is at -4 which means (x+4). I count 4 zeroes but we need 5. We cannot have the remaining zero be imaginary as those always come in pairs. That's why I say that something doesn't add up.